The conic sections
Changes in geometry textbooks over the ages
Perspective in art and projective geometry
Paradoxes in mathematics from Zeno to Russell
The change in the conception of `number'' from the Greek period to the modern one
The notion of function through the centuries
Discussion of a mathematical controversy; e.gZeno's school vs the Aristotelians on indivisibles; Newton vs Berkeley on infinitesimal, Newton vs Leibniz
Mathematics in sub-Saharan Africa
Mathematics in pre-Columbian North America
The ethnomathematics of a particular culture
Consider the history of the limit concept from Eudoxus to the mid-eighteenth century. In particular, consider Berkeley's criticisms and Maclaurin's response
Discuss the development of spherical trigonometry from the Greeks to the Islamic mathematicians. Discuss how and whether one can use this material in trigonometry classes.
Discuss how the history of the solution of cubic equations from the Islamic period through the work of Lagrange can be used in algebra classes at various levels.